A109170 Continued fraction expansion of 2*x which equals the continued fraction of x (A109168) interleaved with positive even numbers.

2, 1, 4, 2, 6, 2, 8, 4, 10, 3, 12, 4, 14, 4, 16, 8, 18, 5, 20, 6, 22, 6, 24, 8, 26, 7, 28, 8, 30, 8, 32, 16, 34, 9, 36, 10, 38, 10, 40, 12, 42, 11, 44, 12, 46, 12, 48, 16, 50, 13, 52, 14, 54, 14, 56, 16, 58, 15, 60, 16, 62, 16, 64, 32, 66, 17, 68, 18, 70, 18, 72, 20, 74, 19, 76, 20, 78

Offset: 1

Author

Paul D. Hanna, Jun 21 2005

Keywords

• cofr
• nonn

Examples

			2*x=2.8169885584578139714969485581613959832279979115641025629325276350497259...
The continued fraction expansion of x = A109168:
[1; 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, ...];
The continued fraction expansion of 2*x = A109170:
[2;1, 4,2, 6,2, 8,4, 10,3, 12,4, 14,4, 16,8, 18,5, ...]
which equals the continued fraction of x interleaved with even numbers.
		

Crossrefs

Cf. A109168 (continued fraction of x), A109169 (digits of x), A109171 (digits of 2*x).

Programs

PARI

a(n)=if(n%2==1,(n+1),if(n%4==2,(n+2)/4,2*a(n/2)))

Formula

For n>=1: a(2*n-1) = 2*n, a(4*n-2) = n, a(4*n) = 2*a(2*n).